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BREAKTHROUGH REPORT21 Aug 2026

BREAKTHROUGH — AI-led disproof of the Yau–Tian–Donaldson conjecture

A new arXiv preprint presents an explicit counterexample to the original cscK Yau–Tian–Donaldson conjecture and documents a strongly AI-led discovery process. Independent mathematical verification is still pending.

ANALYSIS

Methodology note: Historical index values on this Pulse are normalized to the current methodology for comparability. The original as-published record remains unchanged in the canonical archive.

Jihao Liu presents a smooth polarized projective fivefold that is K-polystable but admits no constant-scalar-curvature Kähler metric, which would disprove the original cscK Yau–Tian–Donaldson conjecture. The Fano and uniform/completed variants are explicitly unaffected.

AI role

The paper states that Claude Code (Fable 5), Codex (GPT-5.6 Sol), and Danus produced the counterexample and proof collaboratively. More strikingly, an improved Danus run starting only from the original problem reportedly reproduced a complete counterexample and proof in 5h29m without the key human intervention used in the first run.

Evidence

Primary arXiv preprint, 79 pages, with a detailed appendix on AI use and internal verification records. Independent expert verification is still pending, so this is classified as a high-confidence preliminary breakthrough rather than independently verified.

Score effect

AI for Science 56.9 → 58.1; ASI Readiness 58.4 → 58.8; Singularity Readiness 52.75 → 53.00. Forecast unchanged pending independent verification.